Thousands of the state’s poorest residents are losing or being denied federal housing subsidies as a result of automatic, across-the-board spending cuts, forcing many to choose between food, rent, medicine — or the streets.

The cuts are pummeling the Section 8 voucher program, which offers assistance to poor individuals and families renting apartments in the open market.

The Boston Housing ­Authority, for example, has stopped ­issuing new vouchers after absorbing $10 million in Section 8 voucher cuts, and by fall it could end subsidies for more than 10 percent of the 11,000 households already receiving vouchers.

“Sequestration has been devastating,” said Lydia Agro, a spokeswoman for the BHA. “We’ve never been in this situation — we’ve never had to cut people off the program.”

In Massachusetts, and across the country, groups have protested the cutbacks. Earlier this month, Budget for All, a nonprofit coalition of labor, religious, and peace groups, protested outside Government Center, urging the public to contact US senators who are already planning next year’s federal budget, which begins in October. The group advocates for reducing Pentagon spending and a tax increase on the rich and corporations.

“Everybody says they hate sequester,” said Lee Farris, one of the rally’s organizers. “So Congress needs to find another way between now and when they pass the budget to replace it with what they should have done in the first place.”

The program, begun in the 1970s, offers subsidies to individuals and families who earn no more than 50 percent of the median income in the area they live, though the vast majority earn just 30 percent or less of the median income. In Boston, a family of four with an income of $28,000 a year or less would qualify.

Families with vouchers pay as much as 40 percent of their income toward rent. The program provides a bridge to help many families move out of poverty in a way that helps them avoid the stigma of living in public housing.

India Cox, a single mother living in Mission Hill with her 9-year-old daughter, spent years on the Section 8 waiting list, living in cramped, rundown apartments in unsafe buildings because that was all she could afford. When she recently received a notice that she had been accepted into the Section 8 program, Cox said she felt relieved to finally be able to move and had begun looking for an apartment with a yard or near a park.

But a few weeks later, she received another letter telling her the offer was rescinded because of funding cuts.

“It was snatched away,” said Cox, 29, who works part time taking calls at Blue Cross Blue Shield of Massachusetts. “I’m frustrated. I just wanted to live someplace safer with my daughter.”

Housing specialists said it has never been easy to get a Section 8 voucher, which in the best of times could require years on a waiting list. Linda Wood-Boyle, executive director of HomeStart Inc., a nonprofit that helps homeless families obtain vouchers and other services, said the cuts mean more families with children, elderly, and disabled will struggle with unstable living situations, forced to move from place to place, not knowing where they will sleep some nights.

“People will just stay in shelters longer, or be homeless longer, or doubled-up and couch surfing longer,” she said. “It’s always a problem, but it will just be worse now.”

The state Department of Housing and Community Development, which allocates about 20,000 Section 8 vouchers each year, has a waiting list of about 80,000 low-income households, including about 24,000 people with disabilities.

But federal cuts of more than $12 million mean those individuals and families will stay on the waiting list indefinitely. Matthew T. Sheaff, the agency spokesman, said the state has stopped offering vouchers to new candidates as people leave the program.

Sheaff said the agency is tapping its reserves so it does not have to cut off families who are currently receiving subsidies. “It’s important to keep these people housed,” he said.

However, because of sequestration, the state agency is also facing administrative cutbacks totaling $5.7 million. State officials have not yet implemented reductions due to those cuts.

The BHA has also been told to reduce its administrative spending by $4.6 million and its public housing spending by $10.8 million, Agro said. Thirty-three staffers were recently laid off, there is a hiring freeze, and senior staffers must take five unpaid workdays.

Sue Nohl, deputy director of the Metropolitan Boston Housing Partnership, the state’s largest provider of the vouchers from the state Department of Housing and Community Development, said her agency recently had to notify 43 households that had just been accepted into the program that they would not receive vouchers ­after all, due to cutbacks.

Many had been on the waiting list a decade.

The housing partnership’s program offers about 5,700 vouchers to low-income families every year. They expected to have about 120 vouchers become available this year as ­clients move out of the program as their income increases, die, or violate policies and are terminated. Because of the cuts, they anticipate that they will not be able to offer vouchers to any new clients for at least the next year.

What worries Nohl about the cutbacks is that so many of the people receiving vouchers are already living precariously close to homelessness. The families have so little income that many are forced to choose between paying rent, buying food, or receiving medical care.

“These are people who are making choices not about where to go on vacation, but should I eat today and do we have a place to stay tomorrow,” Nohl said.

Ana Bela Mendes of Dorchester, a divorced mother of three, lost her job of 12 years during the recession and became homeless. She cares for a severely disabled 20-year-old daughter and is taking courses at the University of Phoenix so she can eventually become a nurse. She recently learned that a state subsidy, separate from Section 8, that helped her pay the rent for the past two years will end in the fall.

She said she can’t afford her apartment’s market rate rent of $1,600; her monthly income is $1,100 in child support and disability payments. She had hoped she would get a Section 8 voucher to help her pay for a new place to live, but not anymore.

She said she’ll be lucky to find an affordable one-bedroom, and may have to consider moving out of the city and farther away from her daughter’s doctors.

“I have to scramble and figure out what’s next,” Mendes said. “And I still need to finish school.”

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